COMPLEX STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 329 
TasLE II.—FatiauEe TESTS ON PIERCED PLATES. 
Specimen Width of | Diameter of Endurance, 
Number Plate, Ins. Hole, Ins. N Millions of Cycles. 
1 0-50 0-0365 1-0 0-008 Cracked 
2 1:00 0-100 2:0 0-658 Cracked 
3 1-50 0-066 2-0 0-576 Cracked 
4 1-50 0-100 2:0 0:733 Unbroken (g) 
5 1-50 0-075 3-0 5-446 Unbroken (9) 
6 1-50 0-100 2-1 0-592 Cracked 
7 1:50 0-100 2-1 2-566 Unbroken (9) 
8 1-50 0-066 2-1 1:642 Unbroken (g) 
9 1-50 0-100 2-15 1:126 Cracked 
10 1-50 0-200 2-15 0:772 Cracked 
ll 1-50 0-100 2-2 8-462 Unbroken (9) 
12 1-50 0-0365 2-1 5-660 Unbroken 
os i ania ph és 2-864 Unbroken 
12 1-50 0-0365 2:0 0:986 Cracked 
The statement ‘ Unbroken (g)’ signifies that the test-piece did not crack on the 
pierced section, but did so at the grips. The statement ‘ Cracked ’ signifies failure in 
@ manner appropriate to the investigation, as shown in the photographed specimens— 
fig. 12. The cracks originated at the margin of the hole and spread across the trans- 
verse diametral section. When the crack had extended a certain distance, which 
varied with the value of N, the residual metal failed in a characteristic ductile manner, 
plainly shown by the reflected light from the polished surfaces. 
The photograph shows four pieces from Series II. and one from Series I. ; and in 
each case the development of the fracture in the two distinct stages: (1) by the 
formation of a true fatigue crack, and (2) by subsequent ductile yielding of the 
remaining metal, is clearly shown. 
It is considered that the photograph shows that any ductile yielding that may have 
occurred in stage (1) must have been very slight, and such as did not appreciably 
change the profile of the hole from a circle to an ellipse. Any yielding in this stage 
is probably of the nature which, in a contribution ® to the Report of this Com- 
mittee for 1923, is termed ‘ primary hysteresis.’ While the process of fatigue is 
attributed to ‘secondary hysteresis,’ the action of ‘ primary hysteresis’ is regarded 
as wholly beneficial, being the mechanism by which the stresses are redistributed in 
a more uniform manner than the presence of the hole would initially entail in an 
elastic substance. In metals that show no such primary hysteresis, it is probable 
that no such beneficial redistribution would occur. 
Two conclusions may be drawn at once from the results tabulated, namely :— 
(1) The limiting stresses for failure vary only slightly with the ratio between the 
diameter of the hole and the width of the plate, within the range investigated. 
(2) The presence of the circular hole weakens the hard-drawn strip, subjected to 
pulsating tensile stress, in a manner indicated by the value N = 2:15, instead of by 
the value N = 3-00, as would be anticipated from the mathematical results based on 
the assumption of perfect elasticity. 
Observing that the weakening effect of the hole, in the hard-drawn strip, is inter- 
mediate between the theoretical effect deduced for a perfectly elastic metal and the 
experimental one recorded, for a ductile mild steel, in the communication for 1923,5 
it is inferred that the action of the hole is indeed modified by the redistribution of the 
concentrated stresses, in the manner briefly indicated in 1922. In these circumstances, 
it appears desirable further to develop the argument, and to advance a convenient 
basis for applying the results of mathematical or optical investigations which, in 
their direct application, appear to over-estimate the dangerous effect of a discontinuity 
in a ductile metal subjected to pulsating stress. 
